PSI - Issue 28

8

L.D. Jones et al. / Procedia Structural Integrity 28 (2020) 1856–1874 Author name / Structural Integrity Procedia 00 (2019) 00 – 00

1863

Fig. 4 A schematic of the stress-strain graph of the ductile damage model

In order to define this stress-strain response in Abaqus, four values are needed:  σ 0 : The stress at which failure occurs  ε 1 & σ 1 : Arbitrary stress and strain values > σ 0 and ε 0 , but with the same ratio. This ensures any plastic strain that does accrue has the same elastic modulus as the elastic strain  δ : an arbitrarily small value (we used 1.0 x 10 -15 ) defining the amount of plastic damage that is required to totally damage the bond. The size of this value is greatly exaggerated in Fig. 4

σ 0 : The stress at which failure occurs



 ε 1 & σ 1 : Arbitrary stress and strain values > σ 0 and ε 0 , but with the same ratio. This ensures any plastic strain that does accrue has the same elastic modulus as the elastic strain  δ : an arbitrarily small value (we used 1.0 x 10 -15 ) defining the amount of plastic damage that is required to totally damage the bond. The size of this value is greatly exaggerated in Figure 1 These values are input to Abaqus using the *ELASTIC and *PLASTIC keywords, and using dependencies upon field variables allows for variation from bond to bond of these values. When in compression, a user-defined field subroutine sets the fracture strain to 1.0 x 10 10 , ensuring that fracture does not occur in compression. 3.3. Inertial Response Traditionally in peridynamics, bonds are massless, but Abaqus requires that some mass be assigned to them. In this formulation 1% of mass is assigned to bonds, and 99% to nodes (material points) using the *MASS keyword. Determining the mass to assign to each material point is a trivial matter of determining 99% of the mass of the component and dividing by the number of material points, which is all performed by the meshing pre-processor. The mass assigned to the bonds is slightly more complex, in that the Abaqus input is the density of the truss elements. This requires noting the cross-section of the trusses, A truss , the total length, Σ l i , of all trusses and the mass, m , attributed